Access points along a bezier curve
Would it be practical to use the formula for a Bezier Curve (wikipedia article)?



You can evaluate it for t varying from 0..1.  One complication is that the distance between evaluated points will vary, so if you want constant speed you'll have to compensate by adjusting your time->t mapping.  P0..P3 correspond to the points and handles of each segment of the bezier curve.

Here is a short python example of how to inspect the control points and handles of a bezier curve (in case you are unable to inspect them in the N-panel pop-out of the 3D view):

import bpy

def mission1(curve):
    for spline in curve.splines:
        for kp in spline.bezier_points:
            print("%r"%[kp.handle_left, kp.co, kp.handle_right])
        print("")

mission1(bpy.context.active_object.data)


See also Mathematical formula for Bezier curves  and How can I know the data paths of certain point of bezier curve?